mathematics, a shuffle algebra is a Hopf algebra with a basis corresponding to words on some set, whose product is given by the shuffle product X ⧢ Y of...

device Shuffle!, a 2004 video game and its corresponding anime Shuffle (dominoes), to mix the tiles in dominoes Shuffle algebra, a Hopf algebra with a...

algebra Schur algebra Semisimple algebra Separable algebra Shuffle algebra Sigma-algebra Simple algebra Structurable algebra Supercommutative algebra...

enveloping algebra of a free Lie algebra on a finite set is the shuffle algebra. This essentially follows because universal enveloping algebras have the...

Riffle shuffles may be used to define the shuffle algebra. This is a Hopf algebra where the basis is a set of words, and the product is the shuffle product...

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the...

that the Lyndon words are algebraically independent elements of this shuffle algebra, and generate it; thus, the shuffle algebra is isomorphic to a polynomial...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

who co-founded category theory (with Saunders Mac Lane) and homological algebra. He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent...

began what would become a fruitful collaboration on the interplay between algebra and topology. In 1944 and 1945, he directed Columbia University's Applied...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

be extended to the entire algebra. Examining the lifting in detail, one observes that the coproduct behaves as the shuffle product, essentially because...

In algebra, the Malvenuto–Poirier–Reutenauer Hopf algebra of permutations or MPR Hopf algebra is a Hopf algebra with a basis of all elements of all the...

Clifford algebra is algebra isomorphic to a full matrix ring over R, C, or H (the quaternions), or to a direct sum of two copies of such an algebra, though...

Dridi, Raouf (2019-04-30). "Knuth-Bendix Completion Algorithm and Shuffle Algebras For Compiling NISQ Circuits". arXiv:1905.00129 [quant-ph]. Bernal,...

mathematics, a Grassmann–Cayley algebra is the exterior algebra with an additional product, which may be called the shuffle product or the regressive product...

point is called the shuffle of x and y, and can be extended to higher dimensions. Points can be sorted according to their shuffle without explicitly interleaving...

{\displaystyle (p,q)} shuffles. Loday 2001, p. 45 Dzhumadil'daev, A.S.; Tulenbaev, K.M. (2005). "Nilpotency of Zinbiel algebras". J. Dyn. Control Syst...

quantum field theory, dendriform algebras, associative analogue of the classical Yang–Baxter equation and mixable shuffle product constructions. Let k {\displaystyle...

In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with...

expression. Finally the Nichols algebra is then W n := ∑ σ ∈ S n s ( σ ) : V ⊗ n → V ⊗ n (quantum symmetrizer or quantum shuffle map) {\displaystyle {\mathfrak...

This article uses algebraic notation to describe chess moves. Chess960, also known as Fischer Random Chess, is a chess variant that randomizes the starting...

Blum integer, and a Leyland number. The split Lie algebra E⁠7+1/2⁠ has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous...

over the years. Features include, but are not limited to, menu search, shuffle of questions for randomized order, limiting responses to once per person...

the term Shah function for what is otherwise called a Dirac comb. The shuffle product is often denoted by ш. ש : Hebrew letter ש श: Devanagari letter...

Westerland, Craig (2023-03-05). "Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields". arXiv:1701.04541 [math...

Course in Abstract Algebra, Chapman & Hall/CRC; 2nd edition. ISBN 1-58488-515-7. Fraleigh, John (1993), A first course in abstract algebra (5th ed.), Addison...

In mathematics, the algebraic bracket or Nijenhuis–Richardson bracket is a graded Lie algebra structure on the space of alternating multilinear forms...

elements and perfect shuffle on 2n elements have the same sign; these are important to the classification of Clifford algebras, which are 8-periodic...